A290538 Let S be the sequence generated by these rules: 0 is in S, and if z is in S, then z + 1 and z * (1+i) are in S (where i denotes the imaginary unit), and duplicates are deleted as they occur; a(n) = the square of the norm of the n-th term of S.

0, 1, 4, 2, 9, 8, 5, 4, 16, 18, 13, 16, 10, 10, 5, 8, 25, 32, 25, 36, 20, 26, 17, 32, 17, 20, 13, 20, 10, 5, 16, 36, 50, 41, 64, 34, 50, 37, 72, 29, 40, 29, 52, 34, 25, 64, 26, 34, 25, 40, 26, 17, 40, 9, 20, 10, 9, 32, 49, 72, 61, 100, 52, 82, 65, 128, 45, 68

Offset: 1

Author

Rémy Sigrist, Aug 05 2017

Keywords

• nonn
• look

Comments

See A290536 for the real part of the n-th term of S and additional comments.

See A290537 for the imaginary part of the n-th term of S.

a(n) tends to infinity as n tends to infinity.

Examples

			S(1) = 0 by definition; so a(1) = 0.
S(1)+1 = 1 has not yet occurred; so S(2) = 1 and a(2) = 1.
S(1)*(i+i) = 0 has already occurred.
S(2)+1 = 2 has not yet occurred; so S(3) = 2 and a(3) = 4.
S(2)*(1+i) = 1+i has not yet occurred; so S(4) = 1+i and a(4) = 2.
S(3)+1 = 3 has not yet occurred; so S(5) = 3 and a(5) = 9.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A290538

Crossrefs

Cf. A290536, A290537.

Programs

PARI

\\ See Links section.

Formula

a(n) = A290536(n)^2 + A290537(n)^2.